15. Semisimple Lie algebras

13 novembro 2020, 11:00 • Pedro Resende

Simple Lie algebras. Derived series and lower central series of a Lie algebra, solvable Lie algebras and nilpotent Lie algebras. Reductive Lie algebras and semisimple Lie algebras (defined to be reductive Lie algebras with trivial center, following Brian Hall's book). Decomposition of a reductive Lie algebra as the direct sum of its center and a semisimple Lie algebra. Decomposition of a semisimple Lie algebra as the direct sum of uniquely determined simple Lie subalgebras. Semisimplicity of the complexification of the Lie algebra of a simply connected matrix Lie group. This lecture followed sections 3.2 and 7.1 of Brian Hall's book.